Question

Given f(x)=3x−4 and g(x) = -2x+5, what is (g o f) ⁻¹

A. f∘g
B. g ⁻¹ ∘ f ⁻¹
C. f ⁻¹∘ g ⁻¹
D. g∘ f

Answer 1

To find the inverse of (g o f), we perform the following steps: substitute f(x) into g(x) to get g(f(x)), then find the inverse of g(f(x)), which is (g o f)⁻¹.

Step-by-step explanation:

The composition of functions, denoted as f o g, represents the function obtained by applying the function g to the result of applying the function f. To find the inverse of (g o f), we perform the following steps: substitute f(x) into g(x) to get g(f(x)), then find the inverse of g(f(x)), which is (g o f)⁻¹.

To find (g o f)⁻¹, we need to find the inverse of the composite function.

To find the inverse of (g o f), we perform the following steps:

1. Substitute f(x) into g(x) to get g(f(x)).
2. Find the inverse of g(f(x)), which is (g o f)⁻¹.

So, the correct answer is B. g⁻¹ o f⁻¹.